Question

A uniform disc of mass 2m and radius r is free to rotate in the vertical plane about

Answer 1

                Initial angular momentum of one disc.

L=Iω=

1

2

M

R

2

ω

When another disc. of mass

M

4

and radius R is placed gently on it, total moment of inertia of the combination is

I

′

=

1

2

M

R

2

+

1

2

(

M

4

)

R

2

=

5

8

M

R

2

As no external torque has been applied, angular momentum is conserved.

∴

 

I

′

ω

′

=Iω,

             

ω

′

=

Iω

I

′

1

2

M

R

2

ω

5

8

M

R

2

=

4

5

ω

Answer 2

answer

L=Iω=

1

2

M

R

2

ω

When another disc. of mass

M

4

and radius R is placed gently on it, total moment of inertia of the combination is

I

′

=

1

2

M

R

2

+

1

2

(

M

4

)

R

2

=

5

8

M

R

2

As no external torque has been applied, angular momentum is conserved.

∴

 

I

′

ω

′

=Iω,

             

ω

′

=

Iω

I

′

1

2

M

R

2

ω

5

8

M

R

2

=

4

5

ω